Coolant radiators for motor vehicles with an integrated oil cooler are known, for example from EP-A 0 866 300, DE-A 101 06 515 or DE-A 103 03 542 belonging to the Applicant. The oil cooler or another auxiliary heat exchanger is arranged in one of the coolant boxes, preferably in the coolant outlet box, and its outer face is cooled by the coolant that flows across it. Known oil coolers (DE-C 43 08 858) are designed as disk-type, plate-type or flat tubular heat exchangers. They have an oil inlet pipe connection and an oil outlet pipe connection which are inserted through corresponding openings in the wall of the coolant box and are sealed off. The oil connections are therefore arranged on the outer face of the coolant boxes, which likewise have a coolant inlet or outlet pipe connection. In known cross-flow coolers, in which the coolant tubes are horizontal and the coolant boxes are arranged vertically, the coolant inlet pipe connection is situated at the top on the inlet box, and the coolant outlet pipe connection is arranged at the bottom on the outlet box, so that the flow through the tube/rib block is virtually diagonal. The coolant is able to collect before the outlet pipe connection and is sucked from there by the coolant pump. The oil cooler is therefore arranged above the outlet pipe connection, i.e. the oil inlet and outlet pipe connections are located above the coolant outlet pipe connection. An arrangement of the coolant outlet pipe connection in the lower box area is sometimes not possible, and in this case the outlet pipe connection has been arranged above the integrated oil cooler and its oil connections. In principle, the coolant outlet pipe connection is therefore located outside the oil cooler area and its oil connections. This arrangement has the result that the spacing of the oil connections is relatively small or has to be reduced, depending on the size of the coolant box. In order to provide the required oil cooler efficiency, it is therefore necessary either to increase the number of flow channels (disks, flat tubes), i.e. also make the coolant box higher, or to make the disks or flat tubes wider, which results in a widening of the coolant box or the tube plate. In terms of cost, an oil cooler with a small number of disks and a large spacing of the pipe connections is more favorable.